AP STATS UNIT FIVE

normal random variables

X = context

X~N (mean, sd)

P(X > n) = P(z > (n-mean)/sd) = P(z > z-score)

normalcdf

L: z-score u: 1e99 mean: 0 sd: 1

P(x > n)= answer

normal random variables example problem

heights of young women have a normal distribution with mean 654 inches and standard deviation 2.7 inches. this is a distribution for a large set of data. Now choose one woman at random. (population, SRS)

probability that chosen woman is greater than 65 inches tall?

X = heights of women

X ~ N (64, 2.7)

P(X>65) = P(Z>(65-64/2.7)=P(z>.37)

normalcdf

L: .37 u: 1e99 mean:0 sd: 1

P(x>65)=.3357

combined normal random variables

add/subtract mean

sqrt (sd^2 + sd^2 +sd^2)

-> use these values to solve for z-score

parameter

number that describes an aspect of a population

statistic

number that is computed from sample data often used to estimate unknown

ideal version is population distribution or sampling distribution?

population is ideal; sampling has sampling variability

p vs p hat

p = parameter

p hat = statistic

sampling distribution for a sample proportion

1. state

p = proportion of women who feel they do not get enough time for themselves

P(.45 <= phat <= .49)

n=1025

p=0.47

2. plan

random: random sample was taken

mean: .47

independent: 1025 <= .1(all adult women)

standard deviation = sqrt (p(1-p))/n

normal: np >= 10 n(1-p)>=10

3. do

phat ~ N (mean, sd)

P(stated) -> P(z-score)

normalcdf

sampling distribution for a sample proportion script

The probability that (context) will have a phat (context) is (answer). In the sample, the proportion that (context) is between (context with a probability of (answer)

sampling distribution for differences in proportion

1. state

equations for both

inequality relative to 0

2. plan

normal: do np for both

random: subtract means

sd: sqrt (p(1-p)/n) + (p(1-p)/n)

3. do

P(Pb-Pa > 0) when Pb-Pa ~ N(mean, sd)

P(z > z score)

normalcdf

conclusion for sampling distribution for differences in proportion

the probability that the proportion of context is higher/lower than context is (answer)

mean vs proportion

quantitative vs categorical

central limit theorem (30)

as sample size increases, the distribution of sample means of size n, randomly selected, approaches a normal distribution.

sampling distributions of sample means

same process, different formulas on formula sheet

conclusion: the probability that (context) is greater/below/between than (context) is (answer)

sampling distribution for differences in mean

same as the proportion one just look at formula sheet (idk i lwky gave up its like wtv atp